Repeatable Random Permutation Set

Random permutation set (RPS), as a recently proposed theory, enables powerful information representation by traversing all possible permutations. However, the repetition of items is not allowed in RPS while it is quite common in real life. To address this issue, we propose repeatable random permutation set (${\mathrm{R}}^2\mathrm{P}\mathrm{S}$) which takes the repetition of items into consideration. The right and left junctional sum combination rules are proposed and their properties including consistency, pseudo-Matthew effect and associativity are researched. Based on these properties, a decision support system application is simulated to show the effectiveness of ${\mathrm{R}}^2\mathrm{P}\mathrm{S}$.